If you run Windows 7 or 8 you should be fine since IE11 supports WebGL natively (will some restrictions). If you have an older Windows and IE version like 9 or 10, you have to install either the InstantReality plugin, Flash 11, or Chrome Frame.
Starting with version 9.x of Google Chrome, WebGL is natively supported: http://www.google.com/chrome
Firefox supports WebGL natively. Please always use the latest version of Firefox. You can download the localized builds for your language and platform here: http://www.mozilla.com/firefox/
Mac only: Safari 5.1 and newer on OS X (10.6 and above) include support for WebGL (the Windows version does not). But you still have to enable it through the “Developer” menu. To activate the “Developer” menu go to Preferences->Advanced and check the “Show Developer menu in menu bar” button.
The standard Safari on iOS (8 and above) supports WebGL natively.
Sony Ericsson delivered there 2011 Xperia Phones with WebGL support. By doing so, Sony Ericsson is the second mobile phone manufacturer to support WebGL for the default (Android) web browser and standard HTML content.
Firefox mobile for Android supports WebGL natively. Please use the latest version of Firefox. You can download the localized builds for your language here: http://www.mozilla.org/de/mobile/
Check here if your browser supports X3DOM.
And here you can test if your web browser supports pure WebGL.